What is the standard form of the equation \(4x(x-3)=0\)?
Answer and explanation
Correct answer: \(4x^2-12x=0\)
Expand the factor: \(4x(x-3)=4x\cdot x-4x\cdot3=4x^2-12x\). Thus the standard quadratic form (ax^2+bx+c=0) is \(4x^2-12x=0\). Option B is wrong because the sign is incorrect (+12x instead of -12x). Option C is wrong because the coefficient 4 is missing, and option D is linear (not quadratic). Exam tip: always expand factors first and collect like terms to write the expression as \(ax^2+bx+c=0\).
Frequently asked questions
What is the correct answer to this question?
\(4x^2-12x=0\)
Why is this the correct answer?
Expand the factor: \(4x(x-3)=4x\cdot x-4x\cdot3=4x^2-12x\). Thus the standard quadratic form (ax^2+bx+c=0) is \(4x^2-12x=0\). Option B is wrong because the sign is incorrect (+12x instead of -12x). Option C is wrong because the coefficient 4 is missing, and option D is linear (not quadratic). Exam tip: always expand factors first and collect like terms to write the expression as \(ax^2+bx+c=0\).
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Introduction to Quadratic Equations.
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